Costs Life cycle costs Past and sunk costs Future and opportunity costs Direct, indirect and overhead costs Fixed and variable costs Average and marginal costs

Defining Costs Capital costs Operating costs Development costs Operational costs Maintenance costs By type: By behaviour:By time: By function:  Fixed costs  Variable costs  Recurring costs  Non-recurring costs There are different ways of defining costs:

Life cycle costs Life cycle costs: is the sum of all expenditure associated with the item during its entire service life May include engineering design and development costs, fabrication, testing, operating and maintenance cost as well as disposal cost –First or Initial investment –Operating and maintenance –Disposal cost

Past and sunk costs –Past costs are Historical costs that have occurred –Sunk costs are past costs that are unrecoverable Future and opportunity costs Direct, indirect and overhead cost a.Costs directly attributable to production of good (raw material, labor, machine time) b.Fuel, electricity, office, adm expenses, depreciation of plant etc c.For an Accountant: a are prime or direct and b are indirect or overhead. d.For an Economists: average variable costs, Marginal cost  Fixed and variable costs

Explicit and implicit costs –Explicit :Cost actually involve a transfer of funds (out of pocket expense) –Implicit do not involve an actual cash outflow in the current time period Costs and profits –Accountants: revenue minus all costs –Economist: efficient utilization of resources Resources employed for maximum earning or benefits Ensuring opportunity cost of each resource

A company manufactures 1480 units and accountant provides figures of costs as follows; Economist will convert to average costs Cost of productionTotal costAverage cost Direct labor$ 77,700$ Direct material36, Variable overhead4, TVC118,890AVC80.33 Fixed overheadTFC36,800AFC24.86 Total costTC155,690AC105.19

Cost Structure of Manufacturing Direct material Direct Labor Indirect Material Indirect labor Fixed and misc General and administrative Selling cost Profit Selling Price Conversion Costs Prime Cost Factory Overhead Costs Cost of Manufacturing Cost of Goods Sold

Evaluation Techniques Net present value Pay back method –Conventional –Discounted Internal rate of return Benefit cost ratio

Payback Period How long does it take for the project to generate enough cash to pay for itself? (500) Payback period = 3.33 years

Payback Period: Disadvantages Ignores the time value of money (This problem can be overcome by discounted payback period) Ignores cash flows beyond the cutoff date How to determine the cutoff point? Not consider risk difference Bias for short-term investment

Average Accounting Return Definition for AAR: Average net income / average book value Accept the project if the AAR is greater than a preset rate Disadvantages: Uses an arbitrary cutoff rate, ignores time value of money, and is based on book value rather than CFs and market value

Discounted Cash flow (DCF) Valuation The process of valuing an investment by discounting its future cash flows, including NPV, PI, and IRR Primary investment decision criteria as each of the three methods: –Considers the time value of money, –Examines all net CFs, and –Considers the required rate of return

Net Present Value (NPV) Difference between market value of a project and its cost; NPV = PV of future CFs - initial cost (IC) To get NPV, we will Estimate the required rate of return Estimate the expected future cash flows Find the PV of the CFs and subtract the initial investment

NPV – Decision Rule If NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners NPV is a direct measure of how well this project will meet our goal

,000 70,000 70,000 70,000 70,000 70,000 NPV: Example Suppose we are considering an investment that costs $230,000 and provides annual CFs of $70,000 for five years. The firm’s required rate of return is 12%.

IC = $230,000 k = 12% C (PMT) = $70,000 t = 5 years NPV = PV of future CFs - initial cost (IC) = 70,000 [1 – 1/(1.12) 5 ] /.12 [or 70,000 (PVFA 12%, 5 )] – 230,000 = 70,000 (3.6048) - 230,000 = 252, ,000 = $22,336 By calculator: 12 I/Y PMT 5 N CPT PV =252,  NPV = 252, – 230,000 = $22, Solution:

Is defined as the discount rate at which an investment has a zero net present value. The internal rate of return equates to the interest rate, expressed as a percentage, that would yield the same return if the funds had been invested over the same period of time. Therefore, if the internal rate of return for the project is less than the current bank interest rate it would be more profitable to put the money in the bank than execute the project Internal Rate of Return

IRR is the required return that makes NPV = 0 when it is used as the discount rate Equation: PV of future CFs – IC = 0 –Solve the interest rate and the solved rate is IRR Decision Rule: Accept the project if IRR is greater than the required rate of return; otherwise, reject it

 PV of future CFs – IC = 0 $70,000 [1 – 1/(1 + r) 5 ] / r [or $70,000 (PVFA r, 5 )] - $230,000 = 0 By calculator: Just enter the cash flows as you did with the PV problem and solve for I/Y and that is the IRR: /- PV 12 I/Y PMT 5 N CPT I/Y (IRR) = 15.85% Calculating IRR

NPV vs. IRR In general, NPV and IRR give us the same decision rule, However, IRR is unreliable for ranking: –Nonconventional CFs – CF signs change more than once; IRR may result in multiple answers –Mutually exclusive projects – If you choose one, you can’t choose the other

Mutually Exclusive Projects Period Project A Project B IRR19.43%22.17% NPV With the required return for both projects of 10%,  What is IRR and NPV for each of the projects?  Which project do you accept and why?

Mutually Exclusive Projects Crossover rate (point) –The discount rate that makes the NPVs of two projects equal –Setting the NPVs of the two projects equal and solving for the IRR (r, k), the solved IRR is the crossover rate Crossover rate: Example –Project A’s NPV – Project B’s NPV: 0 = [1/(1 + r) 2 ] –By calculator: 100+/-PV 125FV 2N 0PMT CPT I/Y  11.80%

Mutually Exclusive Projects Decision: –At the rate below 11.80%, choose Project A because of the higher NPV; above 11.80%, choose Project B –In general, for the project with lower IRR, the rate below the crossover rate will lead to higher NPV, and the opposite is the true This can be verified by entering rates around the crossover rate and solving for the two projects’ NPVs

NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.80%

Example For a highway dept, accidents involving motor vehicles on a congested highway has been studied. Calculable costs of accidents embrace lost wages, medical expenses, and property damages. For each fatal accident there are:- –Average non-fatal; 35 accidents –Property damages: 240 Average costs: –Fatality per person :1,200,000 –Non-fatal injury: 42,000 –Property damage: 9,000 Aggregate cost per death: –Fatality per person :1,200,000 –Non-fatal injury (42,000 x 35)= 1,470,000 –Property damage(9,000 x 240)= 2,160,000 –Total=4,830,000

Example Death rate has been 8 per 100 m vehicle-miles Traffic density: 10,000 vehicles per day Cost of money to state is 7 % Two proposals to reduce accidents; –Proposal A; addition of a third lane (center lane for left turning vehicles) –Proposal B; const of a median along with widening of shoulders on both sides Proposal A –Cost per mile = 3,740,000 –Service life = 30 years –Annual maintenance cost will be 3 % of initial cost –Death rate will decrease to 3 per 100 m veh-miles

Example Proposal A –Cost per mile = 3,740,000 –Service life = 30 years –Annual maintenance cost will be 3 % of initial cost –Death rate will decrease to 3 per 100 m veh-miles –Equivalent annual benefit per mile to public is = (8 – 3) ( 10,000 x 365 x $ 4,830,000) / 100 m = $ 881,475 –Annual equivalent cost per mile to the state is (A/P, 7%, 30) = $ 3,740,000 (0.0806) + ($ 3,740,000 (0.03) = $ 413,644 –BC = $ 881,475 / $ 413,644 = 2.13

Example Proposal B –Cost per mile (4 ft median and width by 2 ft) = 3,020,000 –Service life = 30 years –Annual maintenance cost will be 2 % of initial cost –Death rate will decrease to 4 per 100 m veh-miles –Equivalent annual benefit per mile to public is = (8 – 4) ( 10,000 x 365 x $ 4,830,000) / 100 m = $ 705,180 –Annual equivalent cost per mile to the state is (A/P, 7%, 30) = $ 3,020,000 (0.0806) + ($ 3,020,000 (0.02) = $ 303,812 –BC = $ 705,180 / $ 303,812 = 2.32